Dynamics of COVID-19 models with asymptomatic infections and quarantine measures

Considering the propagation characteristics of COVID-19 in different regions, the dynamics analysis and numerical demonstration of long-term and short-term models of COVID-19 are carried out, respectively. The long-term model is devoted to investigate the global stability of COVID-19 model with asymptomatic infections and quarantine measures. By using the limit system of the model and Lyapunov function method, it is shown that the COVID-19-free equilibrium $V^0$ is globally asymptotically stable if the control reproduction number $\mathcal{R}_{c}<1$ and globally attractive if $\mathcal{R}_{c}=1$, which means that COVID-19 will die out; the COVID-19 equilibrium $V^{\ast}$ is globally asymptotically stable if $\mathcal{R}_{c}>1$, which means that COVID-19 will be persistent. In particular, to obtain the local stability of $V^{\ast}$, we use proof by contradiction and the properties of complex modulus with some novel details, and we prove the weak persistence of the system to obtain the global attractivity of $V^{\ast}$. Moreover, the final size of the corresponding short-term model is calculated and the stability of its multiple equilibria is analyzed. Numerical simulations of COVID-19 cases show that quarantine measures and asymptomatic infections have a non-negligible impact on the transmission of COVID-19

Effect of Ga on the Inoxidizability and Wettability of Sn-0.5Ag-0.7Cu-0.05Pr Solder

The effect of trace amount of Ga on the inoxidizability and wettability of Sn-0.5Ag-0.7Cu-0.05Pr solders was investigated systematically by means of microstructure characterizations. The results indicate that the wettability and oxidation resistance properties are remarkably improved with addition of trace amount of Ga. Moreover, it is observed that the trace amount of Ga in Sn-0.5Ag-0.7Cu-0.05Pr solders refines the matrix microstructure. The relationship between wettability and oxidation resistance was put into deep study. And Ga was found to be enriched on the surface of the molten solder, which benefited the properties correspondingly. The results of this study can stimulate the use of low-silver Sn-Ag-Cu-Pr solders for various applications

Water sorptivity of unsaturated fractured sandstone: fractal modeling and neutron radiography experiment

The spontaneous imbibition of water into the matrix and gas-filled fractures of unsaturated porous media is an important phenomenon in many geotechnical applications. Previous studies have focused on the imbibition behavior of water in the matrix, but few works have considered spontaneous imbibition along fractures. In this work, a new fractal model, considering the water losses from the fracture to the matrix, was established to predict the sorptivity of rough-walled fracture. A fractal model, considering the fractal dimension of tortuosity, was modified to estimate the sorptivity of the matrix. Both of the models have a time exponent α and can be simplified to the classical Lucas–Washburn (L–W) equation with α = 0.50. To verify the proposed models, quantitative data on the imbibition of water in both the matrix and the fracture of unsaturated sandstone were acquired by neutron radiography. The results show that the motion of the wetting front in both the matrix and the fracture does not obey the L–W equation. Both theory and experimental observations indicate that fracture can significantly increase spontaneous imbibition in unsaturated sandstone by capillary action. Compared with the classical L–W equation, the models proposed in this study offers a better description of the dynamic imbibition behaviour of water in unsaturated fractured sandstone and, thus, more reliable predictions of the sorptivity of the matrix and the fracture. Moreover, a new method to estimate the time exponent of rough-walled fracture in sandstone was also provided

Effect of In and Pr on the Microstructure and Properties of Low-Silver Filler Metal

The novel low-silver 12AgCuZnSn filler metals containing In and Pr were used for flame brazing of copper and 304 stainless steel in this study. The effects of In and Pr content on the melting temperature, wettability, mechanical properties and microstructure of 12AgCuZnSn filler metal were analyzed. The results indicate that the solidus and liquidus temperatures of filler metals decrease with the addition of In. Trace amounts of Pr have little impact on the melting temperature of the low-silver filler metals. In addition, the spreading area of filler metals on copper and 304 stainless steel is improved. The highest shear strength of brazed joint is 427 MPa when the content of In and Pr are 2 wt.% and 0.15 wt.%, respectively. Moreover, it is observed that the trace amount of Pr significantly refines the microstructure of brazed joint matrix. A bright Pr3Cu4Sn4 phase is found in filler metal and brazing seam when the contents of In and Pr are 5 wt.% and 0.5 wt.%, respectively

Mechanical Property of Sn-58Bi Solder Paste Strengthened by Resin

Sn-58Bi solder has been widely used for microelectronics packaging due to its low melting point temperature, good wetting performance, good mechanical properties, and low cost. Compared with Sn-Bi solder alloy and Sn-Pb solder alloy, the strength and plasticity of Sn-Bi solder are not enough, due to the higher brittleness of bismuth, which thus limits the application of Sn-Bi solder. In order to improve the properties of Sn-Bi solder, a novel solder paste strengthened with resin was developed by mixing epoxy resin (ER) with Sn-58Bi solder, which enhanced the joint strength at a low cost. Aimed at the electronic industry, in this study, the spreadability of the novel solder paste was investigated, and the mechanical properties and microstructure of solder joints after reflow soldering were tested and analyzed. The results showed that when the content of epoxy resin was in the optimum range, the shear strength was significantly higher, reaching nearly twice that of Sn-58Bi solder alone

Comparative Study on the Activity of GaF3 and Ga2O3 Nanoparticle-Doped CsF-AlF3 Flux for Brazing 6061 Al/Q235 Steel Joints

The effect of trace amounts of GaF3 and Ga2O3 nanoparticles on the wettability and spreadability of CsF-AlF3 flux matched Zn-15Al filler metal were comparatively studied on 6061 aluminum alloy and Q235 low-carbon steel. The experimental results indicate that appropriate amounts of GaF3 and Ga2O3 added into the flux could significantly promote the Zn-15Al filler metal to wet and spread on the surface of 6061 aluminum alloy and Q235 low-carbon steel. The optimum ranges for GaF3 and Ga2O3 were 0.0075&ndash;0.01wt.% and 0.009&ndash;0.01 wt.%, respectively. Comparative analysis showed that the activity of CsF-AlF3 flux bearing GaF3 was higher than that bearing Ga2O3. The reason for this is that the former flux has a stronger ability to remove oxides of the base metal and reduce the interfacial tension of the molten filler metal and the base metal

Development of a Novel Low-Silver Cu-P Brazing Filler Metal Bearing Sn

The flame brazing of H62 brass using a novel, low-silver Cu-P brazing filler metal was investigated in this study. The effect of the addition of a trace amount of Sn on the microstructure and properties of Cu-7P-1Ag filler metals was analyzed by means of X-ray diffractometer, scanning electron microscopy and energy dispersive spectrometer. The addition of trace Sn led to a decrease in the solidus and liquidus temperatures of Cu-7P-1Ag filler metals. Meanwhile, the spreading performance of the filler metals on a H62 brass substrate was improved. The microstructure of the low-silver, Cu-P brazing filler metal was mainly composed of α-Ag solid solution, α-Cu solid solution and Cu3P; an increase of Sn content led to the transformation of the microstructure of the joints from a block to a lamellar structure. When the Sn content was 0.5 wt. %, the shear strength of the joint at room temperature reached 348 MPa, and the fracture morphologies changed from a cleavage to a quasi-cleavage structure

Development of a Novel Low-Silver Cu-P Brazing Filler Metal Bearing Sn

The flame brazing of H62 brass using a novel, low-silver Cu-P brazing filler metal was investigated in this study. The effect of the addition of a trace amount of Sn on the microstructure and properties of Cu-7P-1Ag filler metals was analyzed by means of X-ray diffractometer, scanning electron microscopy and energy dispersive spectrometer. The addition of trace Sn led to a decrease in the solidus and liquidus temperatures of Cu-7P-1Ag filler metals. Meanwhile, the spreading performance of the filler metals on a H62 brass substrate was improved. The microstructure of the low-silver, Cu-P brazing filler metal was mainly composed of &alpha;-Ag solid solution, &alpha;-Cu solid solution and Cu3P; an increase of Sn content led to the transformation of the microstructure of the joints from a block to a lamellar structure. When the Sn content was 0.5 wt. %, the shear strength of the joint at room temperature reached 348 MPa, and the fracture morphologies changed from a cleavage to a quasi-cleavage structure

Study on Microstructure and Properties of 12Ag–Cu–Zn–Sn Cadmium-Free Filler Metals with Trace In Addition

The effect of different In contents on the melting characteristics, mechanical properties, and microstructure of 12Ag–Cu–Zn–Sn filler metal was investigated in this paper, and flame brazing of 304 stainless steel and copper plates was done using the 12Ag–Cu–Zn–Sn–xIn filler metal. The results indicate that adding appropriate amount of In can evidently decrease the solidus and liquidus temperatures and improve the wettability of the low silver based filler metals. In addition, the shear strength of 304 stainless steel and copper plates joint brazed by 12Ag–Cu–Zn–Sn–1In are satisfactory due to the solution strength effect, and scanning electron microscopy examination of the braze-zone revealed that more relatively sound joints were obtained when brazing was done with 12Ag–Cu–Zn–Sn–xIn filler metal than with Indium free one; its performance is comparable to that of the joint brazed with the 20Ag–Cu–Zn–Sn filler metal, having a remarkable silver-saving effect

A novel analysis approach of uniform persistence for a COVID-19 model with quarantine and standard incidence rate

A coronavirus disease 2019 (COVID-19) model with quarantine and standard incidence rate is first developed, then a novel analysis approach for finding the ultimate lower bound of COVID-19 infectious individuals is proposed, which means that the COVID-19 pandemic is uniformly persistent if the control reproduction number $\mathcal{R}_{c}>1$. This approach can be applied to other related biomathematical models, and some existing works can be improved by using it. In addition, the COVID-19-free equilibrium $V^0$ is locally asymptotically stable (LAS) if $\mathcal{R}_{c}<1$ and linearly stable if $\mathcal{R}_{c}=1$, respectively; while $V^0$ is unstable if $\mathcal{R}_{c}>1$.Comment: 13 pages, 1 figur